A superadiabatic burner has a flame holder formed from a porous medium, a fuel inlet coupled to the flame holder, a fuel outlet coupled to the flame holder, a preheater comprising an inlet and an outlet coupled to the fuel inlet, and a radiating rod coupled to the porous medium. The porous medium comprises a first porous section and a second porous section. Methods of using the burner allow preheated air or other mixtures to be provided to the fuel inlet as part of a fuel air mixture for the burner.